Coupled Thermoelasticity of Functionally Graded Beams

This paper presents the finite element solution of an Euler–Bernoulli beam with functionally graded material (FGM) subjected to lateral thermal shock loads. The FGM beam is assumed to be graded across the thickness. The material properties across the thickness direction follow the volume fraction of the constitutive materials in power law form. The solution is obtained under coupled thermoelastic assumption. The equation of motion and the conventional coupled energy equation are simultaneously solved to obtain the transverse deflection and temperature distribution in the beam. The governing partial differential equations of the problem are solved simultaneously using the Galerkin finite element method with the C ¹-continuous shape function leading to fast convergence of the solution. Results are presented for different power law indexes and coupling coefficients for simply supported boundary conditions. The results are verified with those reported in the literature.